We propose a probabilistic enhancement of standard kernel Support Vector
Machines for binary classification, in order to address the case when, along
with given data sets, a description of uncertainty (e.g., error bounds) may be
available on each datum. In the present paper, we specifically consider
Gaussian distributions to model uncertainty. Thereby, our data consist of pairs
(xiβ,Ξ£iβ), iβ{1,β¦,N}, along with an indicator
yiββ{β1,1} to declare membership in one of two categories for each pair.
These pairs may be viewed to represent the mean and covariance, respectively,
of random vectors ΞΎiβ taking values in a suitable linear space (typically
Rn). Thus, our setting may also be viewed as a modification of
Support Vector Machines to classify distributions, albeit, at present, only
Gaussian ones. We outline the formalism that allows computing suitable
classifiers via a natural modification of the standard "kernel trick." The main
contribution of this work is to point out a suitable kernel function for
applying Support Vector techniques to the setting of uncertain data for which a
detailed uncertainty description is also available (herein, "Gaussian points").Comment: 6 pages, 6 figure